Question: Which of the following numbers is a factor of 54? ${4,9,10,12,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $54$ by each of our answer choices. $54 \div 4 = 13\text{ R }2$ $54 \div 9 = 6$ $54 \div 10 = 5\text{ R }4$ $54 \div 12 = 4\text{ R }6$ $54 \div 14 = 3\text{ R }12$ The only answer choice that divides into $54$ with no remainder is $9$ $ 6$ $9$ $54$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $54$ $54 = 2\times3\times3\times3 9 = 3\times3$ Therefore the only factor of $54$ out of our choices is $9$. We can say that $54$ is divisible by $9$.